This paper introduces a new approach to classification which combines pairwise decomposition techniques with ideas and tools from fuzzy preference modeling. More specifically, our approach first decomposes a polychotomous classification problem involving m classes into an ensemble of binary problems, one for each ordered pair of classes. The corresponding classifiers are trained on the relevant...

The main theorem of this article is that every countable model of set theory 〈M,∈ 〉, including every well-founded model, is isomorphic to a submodel of its own constructible universe 〈L ,∈ 〉. In other words, there is an embedding j : M → L that is elementary for quantifier-free assertions. It follows from the proof that the countable models of set theory are linearly pre-ordered by embeddabilit...

Dict ionary definitions are logical combina t ions of basic markers. Defini t ions can be reduced to dis junct ions of meanings, which are conjunct ions of markers . T h e set of words which can take on a m e a n i n g is its lexical representation set, and u n d e r natura l condi t ions such sets are partially ordered by inc lus ion in the same way as the mean i ngs are ordered by implicat io...

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

Ralph Freese Department of Mathematics University of Hawaii at Manoa Honolulu, Hawaii 96822 In this paper we look at some of the problems on free lattices and free modular lattices which are of an order theoretic nature. We review some of the known results, give same new results, and present several open problems. Every countable partially ordered set can be order embedded into a countable free...